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Find the value of a and b in each of the following 5+2√3/7+4√3 = a+b√3

Posted by Hitaishi Lilhare 6 years, 7 months ago

CBSE > Class 09 > Mathematics

2 answers

Shaswat Panda 6 years, 7 months ago

a=11 and b=(―6)

0Thank You

Gaurav Seth 6 years, 7 months ago

LHS = (5 + 2√3 ) / ( 7 + 4√3 )

rationalize the denominator

= (5 + 2√3 ) ( 7 - 4√3 ) / [ ( 7 + 4√3 ) ( 7 - 4√3 )

= [ 5 ×7 - 5 × 4√3 + 2√3 × 7 - 2√3 × 4√3 ] / [ (7 )² - (4√3 )² ]
here we used ( x + y ) (x - y ) = x² - y² identity

= [35 -20√3 + 14√3 -24 ] / [ 49 - 48 ]

= (11 - 6√3 )

therefore ,

LHS = RHS

11 - 6√3 = A - B√3

comparing both sides

A = 11,

B = 6

0Thank You

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